{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "SEIR_COVID19.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNKK7FXv9jX6tYy7ctew3Gj",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/alsnhll/SEIR_COVID19/blob/master/SEIR_COVID19.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wAb1ddE0gwhA",
        "colab_type": "text"
      },
      "source": [
        "## Model\n",
        "\n",
        "### Equations\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "\\dot{S} &= -\\beta_1 I_1 S -\\beta_2 I_2 S - \\beta_3 I_3 S\\\\\n",
        "\\dot{E} &=\\beta_1 I_1 S +\\beta_2 I_2 S + \\beta_3 I_3 S - a E \\\\\n",
        "\\dot{I_1} &= a E - \\gamma_1 I_1 - p_1 I_1 \\\\\n",
        "\\dot{I_2} &= p_1 I_1 -\\gamma_2 I_2 - p_2 I_2 \\\\\n",
        "\\dot{I_3} & = p_2 I_2 -\\gamma_3 I_3 - \\mu I_3 \\\\\n",
        "\\dot{R} & = \\gamma_1 I_1 + \\gamma_2 I_2 + \\gamma_3 I_3 \\\\\n",
        "\\dot{D} & = \\mu I_3\n",
        "\\end{split}\n",
        "\\end{equation}\n",
        "\n",
        "### Variables\n",
        "* $S$: Susceptible individuals\n",
        "* $E$: Exposed individuals - infected but not yet infectious or symptomatic\n",
        "* $I_i$: Infected individuals in severity class $i$. Severity increaes with $i$ and we assume individuals must pass through all previous classes\n",
        "  * $I_1$: Mild infection (hospitalization not required)\n",
        "  * $I_2$: Severe infection (hospitalization required)\n",
        "  * $I_3$: Critical infection (ICU required)\n",
        "* $R$: individuals who have recovered from disease and are now immune\n",
        "* $D$: Dead individuals\n",
        "* $N=S+E+I_1+I_2+I_3+R+D$ Total population size (constant)\n",
        "\n",
        "### Parameters\n",
        "* $\\beta_i$ rate at which infected individuals in class $I_i$ contact susceptibles and infect them\n",
        "* $a$ rate of progression from the exposed to infected class\n",
        "* $\\gamma_i$ rate at which infected individuals in class $I_i$ recover from disease and become immune\n",
        "* $p_i$ rate at which infected individuals in class $I_i$ progress to class $I_{I+1}$\n",
        "* $\\mu$ death rate for individuals in the most severe stage of disease\n",
        "\n",
        "### Basic reproductive ratio\n",
        "\n",
        "Idea: $R_0$ is the sum of \n",
        "1. the average number of secondary infections generated from an individual in stage $I_1$\n",
        "2. the probability that an infected individual progresses to $I_2$ multiplied by the average number of secondary infections generated from an individual in stage $I_2$\n",
        "3.  the probability that an infected individual progresses to $I_3$ multiplied by the average number of secondary infections generated from an individual in stage $I_3$\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "R_0 & = N\\frac{\\beta_1}{p_1+\\gamma_1} + \\frac{p_1}{p_1 + \\gamma_1} \\left( \\frac{N \\beta_2}{p_2+\\gamma_2} + \\frac{p_2}{p_2 + \\gamma_2} \\frac{N \\beta_3}{\\mu+\\gamma_3}\\right)\\\\\n",
        "&= N\\frac{\\beta_1}{p_1+\\gamma_1} \\left(1 + \\frac{p_1}{p_2 + \\gamma_2}\\frac{\\beta_2}{\\beta_1} \\left( 1 + \\frac{p_2}{\\mu + \\gamma_3} \\frac{\\beta_3}{\\beta_2} \\right) \\right)\n",
        "\\end{split}\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qxfuhr_4e2TJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np, matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3lxxsmGBiy5X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Defining the differential equations\n",
        "\n",
        "#Don't track S because all variables must add up to 1 \n",
        "#include blank first entry in vector for beta, gamma, p so that indices align in equations and code. \n",
        "#In the future could include recovery or infection from the exposed class (asymptomatics)\n",
        "\n",
        "def seir(y,t,b,a,g,p,u,N): \n",
        "    dy=[0,0,0,0,0,0]\n",
        "    S=N-sum(y);\n",
        "    dy[0]=np.dot(b[1:3],y[1:3])*S-a*y[0] # E\n",
        "    dy[1]= a*y[0]-(g[1]+p[1])*y[1] #I1\n",
        "    dy[2]= p[1]*y[1] -(g[2]+p[2])*y[2] #I2\n",
        "    dy[3]= p[2]*y[2] -(g[3]+u)*y[3] #I3\n",
        "    dy[4]= np.dot(g[1:3],y[1:3]) #R\n",
        "    dy[5]=u*y[3] #D\n",
        "\n",
        "    return dy"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fSBxIqmJqMC4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Define parameters based on clinical observations\n",
        "\n",
        "#I will add sources soon\n",
        "# https://github.com/midas-network/COVID-19/tree/master/parameter_estimates/2019_novel_coronavirus\n",
        "\n",
        "IncubPeriod=5  #Incubation period, days\n",
        "DurMildInf=10 #Duration of mild infections, days\n",
        "FracMild=0.8  #Fraction of infections that are mild\n",
        "FracSevere=0.15 #Fraction of infections that are severe\n",
        "FracCritical=0.05 #Fraction of infections that are critical\n",
        "CFR=0.02 #Case fatality rate (fraction of infections resulting in death)\n",
        "TimeICUDeath=7 #Time from ICU admission to death, days\n",
        "DurHosp=11 #Duration of hospitalization, days\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "54hNLq0QoHXt",
        "colab_type": "code",
        "outputId": "8e3320c9-0bce-4449-af80-52070fe2c19f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Define parameters and run ODE\n",
        "\n",
        "N=1000\n",
        "b=np.zeros(4) #beta\n",
        "g=np.zeros(4) #gamma\n",
        "p=np.zeros(3)\n",
        "\n",
        "a=1/IncubPeriod\n",
        "\n",
        "u=(1/TimeICUDeath)*(CFR/FracCritical)\n",
        "g[3]=(1/TimeICUDeath)-u\n",
        "\n",
        "p[2]=(1/DurHosp)*(FracCritical/(FracCritical+FracSevere))\n",
        "g[2]=(1/DurHosp)-p[2]\n",
        "\n",
        "g[1]=(1/DurMildInf)*FracMild\n",
        "p[1]=(1/DurMildInf)-g[1]\n",
        "\n",
        "#b=2e-4*np.ones(4) # all stages transmit equally\n",
        "b=2.5e-4*np.array([0,1,0,0]) # hospitalized cases don't transmit\n",
        "\n",
        "#Calculate basic reproductive ratio\n",
        "R0=N*((b[1]/(p[1]+g[1]))+(p[1]/(p[1]+g[1]))*(b[2]/(p[2]+g[2])+ (p[2]/(p[2]+g[2]))*(b[3]/(u+g[3]))))\n",
        "print(\"R0 = {0:4.1f}\".format(R0))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R0 =  2.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hj4fS4qguGtJ",
        "colab_type": "code",
        "outputId": "ad57dda1-528a-4762-80e9-31d88e327c7f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "print(b)\n",
        "print(a)\n",
        "print(g)\n",
        "print(p)\n",
        "print(u)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.      0.00025 0.      0.     ]\n",
            "0.2\n",
            "[0.         0.08       0.06818182 0.08571429]\n",
            "[0.         0.02       0.02272727]\n",
            "0.057142857142857134\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QzKEFYi574bZ",
        "colab_type": "code",
        "outputId": "9faacc2f-0c88-4f68-d0da-52dce696715e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "tmax=365\n",
        "tvec=np.arange(0,tmax,0.1)\n",
        "ic=np.zeros(6)\n",
        "ic[0]=1\n",
        "\n",
        "soln=odeint(seir,ic,tvec,args=(b,a,g,p,u,N))\n",
        "soln=np.hstack((N-np.sum(soln,axis=1,keepdims=True),soln))\n",
        "\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(tvec,soln)\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number per 1000 People\")\n",
        "plt.legend((\"S\",\"E\",\"I1\",\"I2\",\"I3\",\"R\",\"D\"))\n",
        "plt.ylim([0,1000])\n",
        "\n",
        "#Same plot but on log scale\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(tvec,soln)\n",
        "plt.semilogy()\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number per 1000 People\")\n",
        "plt.legend((\"S\",\"E\",\"I1\",\"I2\",\"I3\",\"R\",\"D\"))\n",
        "plt.ylim([1,1000])\n",
        "#plt.tight_layout()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 1000)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j4wghupDz7TFwtvr6eq688kpuueUWZs6cee4TDJD1w1KaGhvpP36i08qcOTSS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nDfKhj0FTAvMDDPHgGj74EfbIBJj8DuD+HP4yAvPF9wadFpLJi8gPLacu79+F5OeU6FJV8hhGhP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\nCCGaRSoRQgghhBBCiGb5/3bqZtY+/bVmAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 936x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lUEVUeHHQdyo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# get observed growth rate r (and doubling time) for a particular variable between selected time points\n",
        "#(all infected classes eventually grow at same rate during early infection)\n",
        "\n",
        "#Don't have a simple analytic formula for r for this model due to the complexity of the stages\n",
        "\n",
        "def growth_rate(tvec,soln,t1,t2,i):\n",
        "  i1=np.where(tvec==t1)[0][0]\n",
        "  i2=np.where(tvec==t2)[0][0]\n",
        "  r=(np.log(soln[i2,1])-np.log(soln[i1,1]))/(t2-t1)\n",
        "  DoublingTime=np.log(2)/r\n",
        "\n",
        "  return r, DoublingTime"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sfClhdpsX3o0",
        "colab_type": "code",
        "outputId": "91af2437-9b37-4f4c-c3bb-5a9a912f2491",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "(r,DoublingTime)=growth_rate(tvec,soln,10,20,1)\n",
        "print(\"The epidemic growth rate is = {0:4.2f} per day and the doubling time {1:4.1f} days \".format(r,DoublingTime))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The epidemic growth rate is = 0.08 per day and the doubling time  9.0 days \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d553upzdVzcE",
        "colab_type": "text"
      },
      "source": [
        "### Repeat but with a social distancing measure that reduces transmission rate"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H8QeefcHTjqt",
        "colab_type": "code",
        "outputId": "6ba576cb-c789-4396-b39b-cacb354ef1cf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "source": [
        "bSlow=0.6*b\n",
        "R0Slow=N*((bSlow[1]/(p[1]+g[1]))+(p[1]/(p[1]+g[1]))*(bSlow[2]/(p[2]+g[2])+ (p[2]/(p[2]+g[2]))*(bSlow[3]/(u+g[3]))))\n",
        "\n",
        "solnSlow=odeint(seir,ic,tvec,args=(bSlow,a,g,p,u,N))\n",
        "solnSlow=np.hstack((N-np.sum(solnSlow,axis=1,keepdims=True),solnSlow))\n",
        "\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(tvec,solnSlow)\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number per 1000 People\")\n",
        "plt.legend((\"S\",\"E\",\"I1\",\"I2\",\"I3\",\"R\",\"D\"))\n",
        "plt.ylim([0,1000])\n",
        "\n",
        "#Same plot but on log scale\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(tvec,solnSlow)\n",
        "plt.semilogy()\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number per 1000 People\")\n",
        "plt.legend((\"S\",\"E\",\"I1\",\"I2\",\"I3\",\"R\",\"D\"))\n",
        "plt.ylim([1,1000])\n",
        "\n",
        "(rSlow,DoublingTimeSlow)=growth_rate(tvec,solnSlow,30,40,1)\n",
        "\n",
        "plt.show()\n",
        "print(\"R0 under intervention = {0:4.1f}\".format(R0Slow))\n",
        "print(\"The epidemic growth rate is = {0:4.2f} per day and the doubling time {1:4.1f} days \".format(rSlow,DoublingTimeSlow))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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4A/jA9fpcYJzr8VjXc1yvn6nkSmGimVjMJp69pB+hft7847+rKauuNzqSEEII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\nOE1ZnekdYBDwEfAhMFhrLVc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t9Yo/bc8Eaps1nRCixSmluO3sbnQM8+Ouj9Zx0Ys/89qU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wiFG9fz97tvYeMPCzny/Es5884HCI+W1jKEEH3Hzk0bqC0vZWgXnkI8sfgJ8mvzeXTKo0SHRHe+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\nSBIhhBBCCCGE6BZJIoQQQgghhBDd8v9UXX1f50Zc7wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 936x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "R0 under intervention =  1.5\n",
            "The epidemic growth rate is = 0.03 per day and the doubling time 23.3 days \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l35j9RZIYYaQ",
        "colab_type": "text"
      },
      "source": [
        "#### Compare epidemic growth with and without intervention"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K_AsT2ILYXFV",
        "colab_type": "code",
        "outputId": "986798ab-0044-4f1c-895d-59e349084e79",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        }
      },
      "source": [
        "### All infectious cases (not exposed)\n",
        "\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(tvec,np.sum(soln[:,2:5],axis=1,keepdims=True))\n",
        "plt.plot(tvec,np.sum(solnSlow[:,2:5],axis=1,keepdims=True))\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number per 1000 People\")\n",
        "plt.legend((\"No intervention\",\"Intervention\"))\n",
        "plt.ylim([0,1000])\n",
        "plt.title('All infectious cases')"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'All infectious cases')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8IiKSZLEUJV0UMZkCDAMK4xaRiIgkVSytkiLfy1AKrCIoThIRkUYoljoGvZdB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\nIiISRYlBRESiKDGIiEgUJQYREYny/wHp+TBx7W55lQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6wlkoEkJ_-SO",
        "colab_type": "text"
      },
      "source": [
        "## COVID19 Cases vs Hospital Capacity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9fidHuZmed66",
        "colab_type": "text"
      },
      "source": [
        "Depending on the severity ($I_i$) stage of COVID-19 infection, patients need different level of medical care. \n",
        "\n",
        "Individuals in $I_1$ have \"mild\" infection, meaning they have cough/fever/other flu-like symptoms and may also have mild pneumonia. Mild pneumonia does not require hospitalization, although in many outbreak locations like China and South Korea all symptomatic patients are being hospitalized. This is likely to reduce spread and to monitor these patients in case they rapidly progress to worse outcome. However, it is a huge burden on the health care system.\n",
        "\n",
        "Individuals in $I_2$ have \"severe\" infection, which is categorized medically as having any of the following: \"dyspnea, respiratory frequency 30/min, blood oxygen saturation 93%, partial pressure of arterial oxygen to fraction of inspired oxygen ratio $<$300, lung infiltrates $>$50% within 24 to 48 hours\". These individuals require hospitalization but can be treated on regular wards. They may require supplemental oxygen. \n",
        "\n",
        "Individuals in $I_3$ have \"critical\" infection, which is categorized as having any of the following: \"respiratory failure, septic shock, and/or multiple organ dysfunction or failure\".\n",
        "They require ICU-level care, generally because they need mechanical ventilation. \n",
        "\n",
        "We consider different scenarios for care requirements. One variation between scenarios is whether we include hospitalization for all individuals or only those with severe or critical infection. Another is the care of critical patients. If ICUs are full, hospitals have protocols developed for pandemic influenza to provide mechanical ventilation outside regular ICU facility and staffing requirements. Compared to \"conventional\" ventilation protocols, there are \"contingency\" and \"crisis\" protocols that can be adopted to increase patient loads. These protocols involve increasing patient:staff ratios, using non-ICU beds, and involving non-critical care specialists in patient care. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TSIxDInzALsG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Parameter sources: https://docs.google.com/spreadsheets/d/1zZKKnZ47lqfmUGYDQuWNnzKnh-IDMy15LBaRmrBcjqE\n",
        "\n",
        "# All values are adjusted for increased occupancy due to flu season\n",
        "\n",
        "AvailHospBeds=2.6*(1-0.66*1.1) #Available hospital beds per 1000 ppl in US based on total beds and occupancy\n",
        "AvailICUBeds=0.26*(1-0.68*1.07) #Available ICU beds per 1000 ppl in US, based on total beds and occupancy. Only counts adult not neonatal/pediatric beds\n",
        "ConvVentCap=0.062 #Estimated excess # of patients who could be ventilated in US (per 1000 ppl) using conventional protocols\n",
        "ContVentCap=0.15 #Estimated excess # of patients who could be ventilated in US (per 1000 ppl) using contingency protocols\n",
        "CrisisVentCap=0.42 #Estimated excess # of patients who could be ventilated in US (per 1000 ppl) using crisis protocols\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g_QJMDi-C6c_",
        "colab_type": "text"
      },
      "source": [
        "### Assumptions 1\n",
        "* Only severe or critical cases go to the hospital\n",
        "* All critical cases require ICU care and mechanical ventilation\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2jUXbPcoDWp5",
        "colab_type": "code",
        "outputId": "a43c29fa-8ef7-4983-d38f-7ed9223658b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 344
        }
      },
      "source": [
        "NumHosp=soln[:,3]+soln[:,4]\n",
        "NumICU=soln[:,4]\n",
        "\n",
        "plt.figure(figsize=(13,4.8))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(tvec,NumHosp)\n",
        "plt.plot(np.array((0, tmax)),AvailHospBeds*np.ones(2),color='C0',linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing Hospitalization\",\"Available Hospital Beds\"))\n",
        "ipeakHosp=np.argmax(NumHosp) #find peak\n",
        "peakHosp=10*np.ceil(NumHosp[ipeakHosp]/10)#find time at peak\n",
        "plt.ylim([0,peakHosp])\n",
        "\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(tvec,NumICU,color='C1')\n",
        "plt.plot(np.array((0, tmax)),AvailICUBeds*np.ones(2),color='C1',linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing ICU\",\"Available ICU Beds\"))\n",
        "ipeakICU=np.argmax(NumICU) #find peak\n",
        "peakICU=10*np.ceil(NumICU[ipeakICU]/10)#find time at peak\n",
        "plt.ylim([0,peakICU])\n",
        "plt.ylim([0,10])\n",
        "\n",
        "#Find time when hospitalized cases = capacity\n",
        "icross=np.argmin(np.abs(NumHosp[0:ipeakHosp]-AvailHospBeds)) #find intersection before peak\n",
        "TimeFillBeds=tvec[icross]\n",
        "\n",
        "#Find time when ICU cases = capacity\n",
        "icross=np.argmin(np.abs(NumICU[0:ipeakICU]-AvailICUBeds)) #find intersection before peak\n",
        "TimeFillICU=tvec[icross]\n",
        "\n",
        "plt.show()\n",
        "print(\"Hospital and ICU beds are filled by COVID19 patients after {0:4.1f} and {1:4.1f} days\".format(TimeFillBeds,TimeFillICU))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kokCOcbCkjI17ixnTv+Fdh6qMHxAYoPz55n3hCktEWq82QHszawN0AHbEOB4R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\nlFJKKaVUPff/qtethlXZmFAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 936x345.6 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Hospital and ICU beds are filled by COVID19 patients after 32.2 and 33.2 days\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lyKnREoFmpLk",
        "colab_type": "text"
      },
      "source": [
        "Note that we have not taken into account the limited capacity in the model itself. If hospitals are at capacity, then the death rate will increase, since individuals with severe and critical infection will often die without medical care. The transmission rate will probably also increase, since any informal home-care for these patients will likely not include the level of isolation/precautions used in a hospital."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zPXYpJ1Cd3ev",
        "colab_type": "text"
      },
      "source": [
        "#### Allow for mechanical ventilation outside of ICUs using contingency or crisis capacity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZbAiOqfreQiu",
        "colab_type": "code",
        "outputId": "5532dfb2-9043-43c4-a7ea-60feeb6d6854",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        }
      },
      "source": [
        "plt.plot(tvec,NumICU)\n",
        "plt.plot(np.array((0, tmax)),ConvVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.plot(np.array((0, tmax)),ContVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.plot(np.array((0, tmax)),CrisisVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing Mechanical Ventilation\",\"Conventional Capacity\",\"Contingency Capacity\",\"Crisis Capacity\"))\n",
        "plt.ylim([0,peakICU])\n",
        "plt.ylim([0,10])\n",
        "\n",
        "#Find time when ICU cases = conventional capacity\n",
        "icrossConv=np.argmin(np.abs(NumICU[0:ipeakICU]-ConvVentCap)) #find intersection before peak\n",
        "TimeConvCap=tvec[icrossConv]\n",
        "icrossCont=np.argmin(np.abs(NumICU[0:ipeakICU]-ContVentCap)) #find intersection before peak\n",
        "TimeContCap=tvec[icrossCont]\n",
        "icrossCrisis=np.argmin(np.abs(NumICU[0:ipeakICU]-CrisisVentCap)) #find intersection before peak\n",
        "TimeCrisisCap=tvec[icrossCrisis]\n",
        "\n",
        "plt.show()\n",
        "print(\"Capacity for mechanical ventilation is filled by COVID19 patients after {0:4.1f} (conventional), {1:4.1f} (contingency) and {2:4.1f} (crisis) days\".format(TimeConvCap,TimeContCap,TimeCrisisCap))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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atKkkJCQUmaeqWC6nLXNxztz9ALgByxg/wDhjTE8RedBOf4uUKhHt2rWzthE+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\nKBnh+IMgCErGfx78GOA3eA4LAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Capacity for mechanical ventilation is filled by COVID19 patients after 31.6 (conventional), 42.7 (contingency) and 56.2 (crisis) days\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gADWqf8Ta6oF",
        "colab_type": "text"
      },
      "source": [
        "Compare to the case with intervention"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h6ssC65Ja6F-",
        "colab_type": "code",
        "outputId": "ecf396e6-6173-4098-b2f3-1da712f0e380",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 344
        }
      },
      "source": [
        "NumHospSlow=solnSlow[:,3]+solnSlow[:,4]\n",
        "NumICUSlow=solnSlow[:,4]\n",
        "\n",
        "plt.figure(figsize=(13,4.8))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(tvec,NumHosp)\n",
        "plt.plot(tvec,NumHospSlow,color='C0',linestyle=\"--\")\n",
        "plt.plot(np.array((0, tmax)),AvailHospBeds*np.ones(2),color='C0',linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing Hospitalization\",\"Cases Needing Hospitalization (Intervetion)\",\"Available Hospital Beds\"))\n",
        "plt.ylim([0,peakHosp])\n",
        "\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(tvec,NumICU,color='C1')\n",
        "plt.plot(tvec,NumICUSlow,color='C1',linestyle=\"--\")\n",
        "plt.plot(np.array((0, tmax)),AvailICUBeds*np.ones(2),color='C1',linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing ICU\",\"Cases Needing ICU (Intervetion)\",\"Available ICU Beds\"))\n",
        "plt.ylim([0,peakICU])\n",
        "\n",
        "#Find time when hospitalized cases = capacity\n",
        "ipeakHospSlow=np.argmax(NumHospSlow) #find peak\n",
        "icross=np.argmin(np.abs(NumHospSlow[0:ipeakHospSlow]-AvailHospBeds)) #find intersection before peak\n",
        "TimeFillBedsSlow=tvec[icross]\n",
        "\n",
        "#Find time when ICU cases = capacity\n",
        "ipeakICUSlow=np.argmax(NumICUSlow) #find peak\n",
        "icross=np.argmin(np.abs(NumICUSlow[0:ipeakICU]-AvailICUBeds)) #find intersection before peak\n",
        "TimeFillICUSlow=tvec[icross]\n",
        "\n",
        "plt.show()\n",
        "print(\"With intervention, hospital and ICU beds are filled by COVID19 patients after {0:4.1f} and {1:4.1f} days\".format(TimeFillBedsSlow,TimeFillICUSlow))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XThFCCFFrUikQt0n+OZegbi51Higc6tWe8/kFnM75pZ4jE0LcS5RSXYFZQIjW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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 936x345.6 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "With intervention, hospital and ICU beds are filled by COVID19 patients after 64.4 and 59.2 days\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wdgsujG9ikS0",
        "colab_type": "text"
      },
      "source": [
        "And for expanded mechanical ventilation capacity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DQpzzn9dihXt",
        "colab_type": "code",
        "outputId": "3d136b02-4db9-4b2a-903c-c160340e476a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        }
      },
      "source": [
        "plt.plot(tvec,NumICU)\n",
        "plt.plot(tvec,NumICUSlow)\n",
        "plt.plot(np.array((0, tmax)),ConvVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.plot(np.array((0, tmax)),ContVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.plot(np.array((0, tmax)),CrisisVentCap*np.ones(2),linestyle=\":\")\n",
        "plt.xlabel(\"Time (days)\")\n",
        "plt.ylabel(\"Number Per 1000 People\")\n",
        "plt.legend((\"Cases Needing Mechanical Ventilation\",\"Cases Needing Mechanical Ventilation (Intervention)\",\"Conventional Capacity\",\"Contingency Capacity\",\"Crisis Capacity\"))\n",
        "plt.ylim([0,peakICU])\n",
        "\n",
        "#Find time when ICU cases = conventional capacity (with intervention)\n",
        "icrossConvSlow=np.argmin(np.abs(NumICUSlow[0:ipeakICUSlow]-ConvVentCap)) #find intersection before peak\n",
        "TimeConvCapSlow=tvec[icrossConvSlow]\n",
        "icrossContSlow=np.argmin(np.abs(NumICUSlow[0:ipeakICUSlow]-ContVentCap)) #find intersection before peak\n",
        "TimeContCapSlow=tvec[icrossContSlow]\n",
        "icrossCrisisSlow=np.argmin(np.abs(NumICUSlow[0:ipeakICUSlow]-CrisisVentCap)) #find intersection before peak\n",
        "TimeCrisisCapSlow=tvec[icrossCrisisSlow]\n",
        "\n",
        "plt.show()\n",
        "print(\"Capacity for mechanical ventilation is filled by COVID19 patients after {0:4.1f} (conventional), {1:4.1f} (contingency) and {2:4.1f} (crisis) days\".format(TimeConvCapSlow,TimeContCapSlow,TimeCrisisCapSlow))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xrFmzbKWb9+zZIzn9Ww8aNEgWLlyY4+eQ1Y6IyMqVK2Xw4MEiYiXsevXqSWxs\nrCQlJYmXl5ds3rxZRP4qxZy1PjY2Vs6cOSMNGzaUgwcPZntNVuIXERk9erStnLOISEhIiO0ze+GF\nF2wlrJVyhgIty2yM+RiYgDVT1g5ggjHmI4edgqh8ud6yzHnx9PTE398f+Kts8vnz57l48aKte+X+\n+++3vf7nn39mzpw5+Pv70759e86ePcu+ffty3X9upY6HDh3KkiVLSE1N5csvv2TMmDHX9TnEx8cz\ndOhQvL29eeqpp9i5c6ftud69e1OzZk3Kly/P4MGDbaWYp0+fjp+fHx06dODo0aPs27ePDRs20LVr\nVzw9PQGoUSPvy1hZpZjT09OZP39+ts9HqaIsPzdw9QBaZ/56YIyZDey0v0nJ1GTuX/PKGje3bMsu\n5ctnW3atXDnbcpnq1bMv166d5/4Kuizz9Wxz6dIlu68XET744AP69OmTbX14ePh17b9ChQr07t2b\nRYsW8e233xIZGXnNa7y8vIiMjOTuu+++5rmXXnqJ7t27ExoayuHDh7PdoZtTKebw8HBWrVrF77//\nToUKFQgJCbnhUsz33HMPr732Gj169CAoKIiaNWveUDtKFbb8jOPfDzS+YrlR5jrlYAVdljm3csq5\nqVatGpUrV2bjxo0AtgvMAH369OGTTz4hNTUVsCZAT0xMzLUte6WOx44dy9///nfatWtH9erVr9n2\n8ccfZ/bs2bY4AH744QdOnz5NfHw8DRo0AGDWrFnZtlu5ciVxcXFcunSJhQsX0rlzZ+Lj46levToV\nKlRg9+7dbNiwAbDKU69Zs4ZDhw4BEBcXd00cV39+7u7u9OnTh0ceeURLMatiJT+JvzLwhzEm3BgT\nDuwCqhhjfjTG/OjQ6Eq5gi7LPH78ePr27Uv37t3zHcMXX3zBuHHj8Pf3JzExkapVqwJWsm7Tpg2B\ngYF4e3vz8MMP2z2yt1fqOCgoiCpVquSaPOvWrcu8efN45plnaNmyJa1bt2bFihVUrlyZ5557jhde\neIGAgIBr9h8cHMw999yDr68v99xzD23btqVv376kpaXRunVrnn/+eTp06ABY5ak/++wzBg8ejJ+f\nH/fdd981cQwbNox3332XgIAADhw4AFilmF1cXLj99tvz/Zkq5Wx5lmU2xtidSUNEcp4OqQBpWWbn\nSUhIoFKlSgBMnjyZkydP8v777xfoPk6cOEFISAi7d+/GxaVgpoiYNWsWERERfPjhhwXSXm6mTJlC\nfHw8b7zxhkP3o1ReCrQss4isNsbU5a9qnJtE5EyBRKqKvKVLl/L222+TlpZGkyZNrulOuVlz5sxh\n0qRJvPfeewWW9AvLoEGDODSmHe0AACAASURBVHDgAL/++quzQ1HquuTniP9e4F0gHOtmri7AsyJy\n/Vcdb5Ae8SullH0FesQPTALaZR3lZ1bnXAUUWuJXSilVcPJzbu1yVdfO2Xxup5RSqgjKzxH/T8aY\nFVhF2sCaK3e540JSSinlSPm5uPusMWYwcFvmqs9EJNSxYSmllHKU/HbZRALLROSfwApjTGUHxqSu\ncD1lmTt16mS3restwzxlyhRatWqFv78/7dq1Y86cOXlvVADGjh1rK3/873/rnD9KFbT81OoZh3Uh\nd0bmqgbAQkcGpSySWZY5JCSEAwcOEBkZydtvv83p06ezvS7rxqX169fbbW/ZsmVUq1YtX/v+9NNP\nWblyJZs2bWLLli388ssv5DUCrKB8/vnnttLHmviVKnj5OeJ/DOgMXAAQkX1AHUcGpSxhYWG4ubkx\nYcIE2zo/Pz+6dOlCeHg4Xbp0YcCAAbYkmXWj1cmTJ+natSv+/v54e3uzdu1aADw8PIiNjSUxMZF+\n/frh5+eHt7c38+fPv2bf//73v/nkk0+oUqUKYBVVGz16NACvv/467dq1w9vbm/Hjx9t+EEJCQnjy\nySdt+920aRNgTaLSsWNHAgIC6NSpE3v27AEgPT2dZ555Bm9vb3x9ffnggw9s7URERPD8889z6dIl\n/P39GTFiBC+//DLTpk2zxThp0qQCv5lMqVIhp5KdVz6AjZl/Rmf+WQbYltd2BfkoKmWZf5gSKbvW\nnRARkbS0dPlhSqTs3nBSRERSLqfJD1MiZe/mUyIikpyUKj9MiZT9UadFRCTp4mX5YUqkHNxqlUVO\nOJ+c5/7tlWUOCwuTChUq2MoIi4hUrFhRRESmTJkib775ZmacaXLhwgUR+asM84IFC2Ts2LG27c6f\nP5+t7fj4eKlWrVqucWWVLBYRGTlypPz4448iItKtWzdbu6tXr7aVcM6tdPLHH38s99xzj+25rHa7\ndetmK6Gc9Z5ERA4dOmSreZ+eni5NmzaV2NjYXONUqjS5nrLM+RnVs9oY8y+gvDGmN/AosNgxP0Pq\negQHB9vKCF+pXbt2PPTQQ6SmpjJw4EBbueUsPj4+PP3000ycOJG77rqLLl26XNd+w8LCeOedd0hK\nSiIuLg4vLy/69+8PwPDhwwHo2rUrFy5csJV2Hj16NPv27cMYYyvstmrVKiZMmECZMtbXMK9SyB4e\nHtSsWZPo6GhOnz5NQECAVsRU6gbkp6vneSAGqx7/w8Ay4EVHBlVUDXo6kNad6gPg6urCoKcDadne\nKozmVtaVQU8H0rxtXQDKlS/DoKcDaRZg9YqVr1SWQU8H4ulbC4CKVcvlsIfsssoR56ZixYo5ru/a\ntStr1qyhQYMGjBkz5pqLsi1atCAqKgofHx9efPFFXn/99WzPV6lShUqVKnHw4MFr2k5OTubRRx9l\nwYIFbN++nXHjxmUra5xTKeSs0sk7duxg8eLFN1wGGawLv7NmzWLmzJk89NBDN9yOUqWZ3cRvjPHH\nmn3rNxEZKiJDROR/macQysHslWW258iRI9StW5dx48YxduxYoqKisj1/4sQJKlSowMiRI3n22Wev\neR7ghRde4LHHHuPChQuAVaxtzpw5tqRdq1YtEhISrpkvIOt6wW+//UbVqlWpWrVqrqWTe/fuzYwZ\nM2wXp3Mqhezm5mY7QwCrPs5PP/3E5s2br5kLQCmVP7l29RhjXgZGYg3lfMcY87aI/K/QIlO2ssz/\n+Mc/+M9//oO7uzseHh5MmzaN48eP57pdeHg47777Lm5ublSqVOmaI/7t27fz7LPP4uLigpubG598\n8sk1bTzyyCMkJCTQrl073NzccHNz4+mnn6ZatWqMGzcOb29v6tWrZ5tRK4u7uzsBAQG2GbUAnnvu\nOUaPHs2bb75Jv379bK8dO3Yse/fuxdfXFzc3N8aNG8fjjz+erb3x48fj6+tLYGAgX3/9NWXLlqV7\n9+5Uq1YNV1fX6/5MlVJ2irQZY3Zi1ehJMsbUBH4SkXY5vtjBtEhb8RASEsKUKVNo2/aamlAFJiMj\ng8DAQL777juaN2/usP0oVdxcT5E2e109l0UkCUBEtD6Pcrpdu3Zx66230rNnT036St0Ee6N6ml4x\nw5YBml0545aIDHBoZKrYCQ8Pd2j7bdq0yfGCs1Lq+thL/FfPbD3FkYEUVSJyzUgVpZQqSq53vE2u\niV8KYUrFos7d3Z2zZ89Ss2ZNTf5KqSJJRDh79izu7u753iY/N3CVWg0bNuTYsWPExMQ4OxSllMqV\nu7s7DRs2zPfrnZL4jTHVgM8Bb0CAh0Tkd2fEYo+bm1uOd8YqpVRx5qwj/vexhocOMcaUBSo4KQ6l\nlCp1ch2iaYypaoyZbIzZbYyJM8acNcb8kbkuf7V9c2kX6Ap8ASAiKSKS/yLxSimlboq9sfnfAueA\nEBGpISI1ge6Z6769iX16YtX+mWmMiTbGfG6MuabojDFmvDEmwhgToX3sSilVcOwlfg8R+Y+InMpa\nISKnROQ/QJOb2GcZIBD4REQCgESsQnDZiMhnItJWRNrWrl37JnanlFLqSvYS/xFjzHPGmLpZK4wx\ndY0xE4GjN7HPY8AxEdmYubwA64dAKaVUIbCX+O8DamLV4z9njDkHhAM1gHtvdIeZZxBHjTEtM1f1\nBHbdaHtKKaWuj70buM4BEzMfBe0J4OvMET0HgQcdsA+llFI5sDuc0xjTBxiINcE6wHFgkYj8dDM7\nFZEtgONKOCqllMqVvXr804AWwBysfnmAhsDfjTF3iMiThRCfUkqpAmbviP9OEWlx9UpjzHxgL6CJ\nXymliiF7F3eTjTE5TbzSDrjxSVOVUko5lb0j/jHAJ8aYyvzV1dMIiM98TimlVDFkb1RPFNDeGFOP\nKy7uXnlDl1JKqeInr1E9VYFuXJH4jTErtLaOUkoVX/aKtD0ARAEhWNUzK2DV6onMfE4ppVQxZO+I\nfxIQdPXRvTGmOrARa5inUkqpYsbeqB6DNUnK1TIyn1NKKVUM2TvifwuIMsb8zF9F2RoDvYE3HB2Y\nUkopx8j1iF9EZmOVVVgNXM58hANtRWRWYQSnlFKq4Nkd1ZNZqG1eIcWilFKqENjr48+VMWZ7QQei\nlFKqcNgr0jY4t6eAeo4JRymllKPZ6+qZD3xNziN73B0TjlJKKUezl/i3AVNEZMfVTxhjejkuJKWU\nUo5kr4//H8CFXJ4b5IBYlFJKFQJ7RdrW2nkuwjHhKKWUcrQbGtWjlFKq+NLEr5RSpYzdxG+McTHG\n3FtYwSillHK8vO7czTDGPAd8W0jxqGLqcGwivx88S0JyGrfWqUTHZjVxd3N1dlhKqRzYTfyZVhlj\nnsEa15+YtVJE4hwWlSo24hJTeHnRDpZsO5ltfe3K5XiuT0uGBDXEGC3mqlRRkp/Ef1/mn49dsU6A\npgUfjipOjpxNZPhnG4hNSOGJHrdyT2BDqlcoS9TRc3z0636eXbCNzYfj+PcgH8q46uUkpYqKPBO/\niHgWRiCqeDlzIZnhn23gUmo6Cx7piG/DarbnuresQ9fmtZm2ai8f/LqflLQM/nufvx75K1VE5Jn4\njTEVgH8CjUVkvDGmOdBSRJY4PDpVJKWlZ/D4/0VzLimV7yZ0xLtB1Wte4+piePr2lpQr48KUn/fi\nWasST/Zq7oRolVJXy8/590wgBeiUuXwceNNhEaki75PwA2w6HMfbg31yTPpXeqy71QX031V7Wbsv\nppAiVErZk5/E30xE3gFSAUQkCZ16sdQ6HJvIB2H76edTn4EBDfJ8vTGGtwZ5c2udSjz73Tbik1IL\nIUqllD35SfwpxpjyZFbpNMY0w5qNS5VCry3eSVlXF17u3ybf27i7ufLfe/2JTbjMW8t2OTA6pVR+\n5Cfxvwr8BDQyxnwN/AI858igVNG0+XAcYXtieKLHrdStcn2VuX0aVuWh2zz5NuIYW46ed1CESqn8\nyDPxi8jPwGBgDPAN1py74Y4NSxVFU3/eQ+3K5Xigo8cNbf9Ej1upU7kcryzaQUZGTtM8KKUKQ66J\n3xhTxxgzzRizBHgGWCsiS0QktvDCU0XF+gOxbDgYx6MhzShf9sbuyK3s7sYLd7Zi67F4Fm87UcAR\nKqXyy94R/xysO3U/ACoB0wslIlUk/W/NQWpVKsfw4MY31c7dfg1oVa8y01btIy09o4CiU0pdD3uJ\nv76ITBKRFSLyBOBbWEGpouVgTAJhe2IY2aHxTdffcckc338oNpEfoo4XUIRKqeuRV3XO6saYGsaY\nGoDrVcuqlJi1/jBlXV0Y0b5JgbTXq3Ud/BpV4/1f9pGSpkf9ShU2e4m/KhB5xaMKEJX595uegcsY\n42qMic68hqCKqPhLqSyIPMYA/1uoXblcgbRpjOGpXs05fv4SC7foUb9Shc3e1IseDt73k8AfWD8o\nqohavPUESSnpjL7BkTy56daiNq3rV+GzNQcZEtgQFxe9J1CpwuKUkonGmIZAP+BzZ+xf5d93EUdp\nVa8y3g0K9vfZGMOEbk3ZfyaBX3afKdC2lVL2OatW7jSsm8By7eA1xow3xkQYYyJiYrTGizPsPnWB\nrcfiubdtI4dU1uznU58G1cozY/WBAm9bKZW7Qk/8xpi7gDMiEmnvdSLymYi0FZG2tWvXLqTo1JW+\niziGm6vJV02eG1HG1YVxXTyJOHKOyCM6r49ShSWvUT2uxpjdBbzPzsAAY8xhYB7QwxjzVQHvQ92k\nlLQMFkYfp1frutSoWNZh+7m3XSOquJfhy3WHHbYPpVR2dhO/iKQDe4wxN3fXTvY2XxCRhpkXj4cB\nv4rIyIJqXxWMtftiOJuYwtC2DR26nwply3Bfu0b8tOMUp+KTHbovpZQlP1091YGdxphfjDE/Zj0c\nHZhyruU7TlHZvQy33er4brZRHTzIEOHrjUccvi+lVP7m3H3JUTvPLPYW7qj21Y1JTc9g5a7T9G5d\nl7JlHH8ZqHHNCvRsVYdvNv3J4z1upVyZm7s7WCllX36qc64GDgNumX/fjHUjlyqhNhw8S/ylVPp6\n1yu0fY7u5EFsQgrLtp8stH0qVVrlmfiNMeOABcCMzFUNgIWODEo51/Idp6hQ1pWuLQpvNNVtt9ai\nae2KzFqv3T1KOVp+zuMfwxqJcwFARPYBdRwZlHKe9Azh552n6d6yzk0XZLsexhhGd/Rg69HzOlGL\nUg6Wn8R/WURSshaMMWXInIZRlTyRR84Rm3C5ULt5stwT1JCKZV2Z8/vhQt+3UqVJfhL/amPMv4Dy\nxpjewHfAYseGpZxl+Y6TlC3jQvdWhX9SV6lcGQYHNmTJtpPEJabkvYFS6obkJ/E/D8QA24GHgWXA\ni44MSjmHiLBixym6Nq9NpXL5GfBV8EZ1bEJKWgbfRhx1yv6VKg3yM6onA5gNvAG8BswWEe3qKYG2\nHYvnRHyyU7p5srSoW5n2njX4euMR0nVeXqUcIj+jevoBB7CmXvwQ2G+MucPRganCt3zHKcq4GHq3\nruvUOB7o6MHRuEus3qtVO5VyhPx09UwFuotIiIh0A7oD/3VsWKqwiQg/7ThJx2Y1qVrBzamx3O5V\nl9qVyzH3dx3aqZQj5CfxXxSR/VcsHwQuOige5SS7T13k8Nkkp3bzZHFzdWF4cGPC98bw59kkZ4ej\nVImTa+I3xgw2xgwGIowxy4wxY4wxo7FG9GwutAhVofhpxymMgdvbOD/xA9wf3BgXY7R+j1IOYO+I\nv3/mwx04DXQDQrBG+JR3eGSqUP204xTtPGoU2Ly6N6teVXdub1OX+RFHSU5Nd3Y4SpUo9ubcfbAw\nA1HOczAmgT2nL/JK/zbODiWbUR2bsHzHKZZsO8mQIMeWh1aqNMlzsLYxxhN4AvC48vUiMsBxYanC\ntHzHKQD6eBWNbp4sHZvWpFntiszdcEQTv1IFKD936SwEvsDq2891jlxVfK3YeQq/RtW4pVrR6sEz\nxjCqQxNeXbyLbcfO49uwmrNDUqpEyM+onmQRmS4iYSKyOuvh8MhUoTh2Loltx+K5owiM5snJ4KCG\nVCjrqkM7lSpA+Un87xtjXjHGdDTGBGY9HB6ZKhQ/ZXbz9C1i3TxZqri7MTCgAT9uPcH5JK3fo1RB\nyE/i9wHGAZOxbuaaCkxxZFCq8Py04xSt6lXGo1ZFZ4eSq1EdmnA5LYPvIo45OxSlSoT8JP6hQFMR\n6SYi3TMfPRwdmHK8MxeSifzzHHd413d2KHa1rl+Fdh7V+WrjETK0fo9SNy0/iX8HoFfVSqAVu04j\nAnf4FM1uniuN6ujBkbNJrNkX4+xQlCr28jOqpxqw2xizGbictVKHcxZ/P+04SdPaFWlep5KzQ8lT\nX6961KpUlq82HCGkpU4Ap9TNyE/if8XhUahCdy4xhQ0H43i4a1OMMc4OJ09ly7gwrF1jPgrfz9G4\nJBrVqODskJQqtvJTj391To/CCE45zso/TpOeIUW+f/9K97dvjAH+b9Ofzg5FqWItP/X4LxpjLmQ+\nko0x6caYC4URnHKcn3acokG18ng3qOLsUPLtlmrl6dW6LvM3H+VymtbvUepG5eeIv7KIVBGRKljF\n2e4BPnZ4ZMphLian8tu+WPp61ysW3TxXeqCjB3GJKSzbftLZoShVbOVnVI+NWBYCfRwUjyoEv+4+\nQ0p6RpG9W9eeTs1q0rRWRb2TV6mbkJ8ibYOvWHQB2gLJDotIOdyy7SepW6UcgY2rOzuU6+biYhjR\noQlvLNnFjuPxeDeo6uyQlCp28nPE3/+KRx+s2bfudmRQynESL6cRvieGO7zr4+JSvLp5sgwJaoi7\nmwtfbdCjfqVuRJ5H/FqXv2T5dfcZLqcVz26eLFXLuzHQvwELtxznhTtbU7W8c+cIVqq4yTXxG2Ne\ntrOdiMgbDohHOdjyHSepXbkcbT1qODuUmzKqYxPmbT7Kgshj/O02T2eHo1SxYq+rJzGHB8DfgIkO\njks5QFJKGr/uPkNfr3q4FtNunixet1QlsHE1vtqg9XuUul65Jn4RmZr1AD7DGsr5IDAPaFpI8akC\nFL4nhuTUjGJRmyc/RnVswqHYRNYdiHV2KEoVK3Yv7hpjahhj3gS2YXULBYrIRBE5UyjRqQK1dPtJ\nalYsS3vPms4OpUDc6VOfGhXLMnu9XuRV6nrkmviNMe8Cm7FG8fiIyKsicq7QIlMF6lJKOmG7z9DH\nu/h382QpV8aVke0bs+qP0+w7fdHZ4ShVbNg74n8auAV4EThxRdmGizdTssEY08gYE2aM2WWM2WmM\nefJG21L5t3rvGZJS0rmzGNXmyY8xnT0p7+bKJ6sPODsUpYoNe338LiJS/sqSDZmPypnlG25UGvC0\niLQBOgCPGWPa3ER7Kh8WRp+gVqVydGhavEfzXK1GxbIMD27Moi0nOBqX5OxwlCoWrqtkQ0EQkZMi\nEpX594vAH0CDwo6jNIlPSuXX3Wfo71efMq6F/k/ucOO6euJi4LM1B50dilLFglOzgDHGAwgANubw\n3HhjTIQxJiImRmdduhnLd5wkJT2DQQEl8/e1ftXy3BPYkPkRRzlzUauJKJUXpyV+Y0wl4HvgHyJy\nzTUDEflMRNqKSNvatWsXfoAlSGj0cZrWqohPCa5r83C3ZqSlZ/DFb4ecHYpSRZ5TEr8xxg0r6X8t\nIj84I4bS4vj5S2w8FMfd/g2KXQnm6+FZqyL9fG9h7u9HiE24nPcGSpVihZ74jZV9vgD+EJH3Cnv/\npc2PW04AMDDgFidH4nj/6NWc5NR0PgnXET5K2eOMI/7OwCighzFmS+bjTifEUeKJCKHRxwhoXI0m\nNSs6OxyHa1a7EvcENmTuhiOcjL/k7HCUKrKcMarnNxExIuIrIv6Zj2WFHUdpEH30PHtPJzA0qJGz\nQyk0f+/ZHBFh+i/7nR2KUkVWyRvbp2zmbzpKeTdX+vuVrJu27GlUowLDgxvzXcRRjpxNzHsDpUoh\nTfwlVMLlNBZvO0F/v/pUdi9d9eof734rZVwN767Y4+xQlCqSNPGXUIu3niApJZ1hwY2dHUqhq1PF\nnfFdm7Fk20kiDsc5OxylihxN/CXUvE1/0qJuJQIaVXN2KE4xoVtT6lVx57XFu7Rev1JX0cRfAm0/\nFs/WY/EMa9e4RI/dt6dC2TJMvKMl24/H833UMWeHo1SRkuecu6r4+XLdISqWdWVI24bODsWp7vZr\nwOz1R3hnxR7u8KlPpXJF5OueFAdnD0DCKUg4DQln4NI5SEuGtMvWn8YVyrhDmXLgVgEq1oJKdaBS\nXajSAGo0BTd3Z78TVUwVkf8JqqCcuZDMkm0nGNG+CVVK2UXdq7m4GF7p34bBn6xnyoo9vDrAq3AD\nyMiA2D1wLAKOR0LMbojdC0lnr3qhAfeq4FbeSvSu5UAy/voRSEmE1KtHKBmo1ghqNoe6XtAgEG4J\nhGqNoZSe5an808Rfwny14QhpGcKYTh7ODqVICGhcnZHtmzD798MMDGiAvyOveYjA6Z1wMAwOhMGx\nzXA5swxVuapWgm51F9RqDjVvhSq3WEfwFWqBax7/FVOSIPGMdXZw/k84ux9i98HZfbDxU0hPsV5X\noSY06gBNu4FnN6jdUn8I1DU08ZcgyanpfL3xT3q2qotHrZJ/p25+Pde3JSt3neb577ex+InbcCvI\n0tSpl2D/L7B7CRz41eq6AajVEnyGQMN21qNGM3C5if2WrQBlPaC6BzQKzv5cWgqc3gEnouB4FBz+\nDfYstZ6rVBeahkDLO+DWXlCu8o3HoEoMTfwlyHcRRzmbmMLfbvN0dihFSmV3N16/24vxcyP5bM1B\nHut+6801mJII+1bCrkWwd4XVDeNeDW7tCc16QNPuULUQS2CXKWt19TQIhHaZ684dhkNr4dBqK9Zt\n88G1LHh2hZZ3Qqt+ULle4cWoihQjUvSHurVt21YiIiKcHUaRlpKWQci7YdxSrTzfTehYakfz2PPo\n15Gs2nWG0Mc64XXLDZSoPrUdIr6Ebd9CSoLVRdP6LmhzN3h0Adciek0lIx2OboTdS2HPMog7CBjw\n7ALeQ6DNAChf3dlRKgcwxkSKSNtr1mviLxm+2fQnL/ywndkPBdOthc5fkJO4xBT6TltDlfJuLHni\nNtzdXPPeKPUS7FxoJfxjm6yRNl6DwW8YNOmcd998USNiXWTeuRC2fwdxB8DFDZr3trqmWtxhdSup\nEkETfwmWmp5Bj6nh1KhQloWPddajfTvW7I3hgS83MbpjE1672zv3F8bug4iZsOVrSD5vXYxt+xD4\nDYcKJWTeYhE4EQ07vrceF09CuSrgPRgCRkGDIL0wXMzllviL2eGKysm8zUc5GneJV/t7adLPQ9cW\ntXmosydfrjtE51trcbvXFf3caSnWRdGIL+HQGnApA637Wwnfo0vJS4LG/HVtoPfr1kXhrd/A1vkQ\nOQtqtwL/EdbZTaU6zo5WFSA94i/mLian0n1KOE1rV2L++A6a+PMhOTWde2f8zsGYRBY93plmbnFW\noouaaw2ZrNoYgkZbR72V6zo73MKXfAF2hkL0V1b3lksZaN4HAkZaXUJF9VqGuoYe8ZdQM1YfJDYh\nhS9Gt9akn0/ubq58cr8/73z4ATEz3qFpWiQGoEUfaPs3a3SOSz76/0sq9yrWD1/QaIjZY3V3bZ1n\nnQ1VrAN+91k/irVbOjtSdYP0iL8YOxqXRO//rub2NvWYPjzA2eEUDxdPWUf2UbMh/ihnpBqbqt/F\nHQ88h2uNJs6OruhKT4P9K62zgL0/QUaadX9CwEjrYrd7FWdHqHKgR/wljIjw8qIduBjDxDtaOTuc\noi0jAw6vsfrudy+1kpZnN+jzFsvPtuaVpfsYteYir98tetaUG9cy1k1gLe+AhBjrvoDoubD4SVj+\nPHgNtH4EmnQueddCSiBN/MXUsu2nCNsTw4v9WtOgWnlnh1M0JcVZ3RQRM61hi+WrQ/sJEPQg1LJu\n4hoNnLiYzow1B6lX1f3mb+4qDSrVhk6PQ8fHrDuFo+dao4K2fgPVPa0Lwv7DoWrpLhJYlGlXTzEU\nl5hCn2lrqFulHAsf7UyZgixBUNyJWDcrRcy0LlCmX4ZG7a2++zZ351jRMiND+Oe3W1i45QSv3+3F\nAx09Cj/u4i4lySpbET3XGhGFse5iDhhp3SVcppyzIyyVtKunhBARJn6/jfikVGY92E6TfpakOOsC\nZOQsqyJm2coQOMo6uq9nZ7w+VhXPd4b4kXA5nZcX7SQtXXhIy15cn7IVwPde63HuMGz5P4j+GhY8\naJ1p+Qy1zgTq+2lXUBGgR/zFzNcbjzApdAcv9mvN2C5NnR2Oc4nAkfVWst+1yDq6b9DWGo3iNRjK\nVbqu5lLSMnjimyhW7DzNC3e0YnzXptrnfzMy0q1aQdFfwR9LrH+fWi2sMhE+Q6BmM2dHWOLpnbsl\nwJaj57l3xu+096zB7AeDcXEppUkp/jhs/9Y6qozda91t6nuflfDr+dxU06npGfxj/haWbjvJ6I5N\neLm/F66l9XMuSElxsGshbP8ejqwDxDr69x5i3Sms1wMcQhN/MXcy/hIDPlxHuTIu/Pj4bdSoWNbZ\nIRWuyxdh14+wbZ5VdRKx6s4HjYY2Awu0vkx6hvD2sj/4/LdD9GxVh/eHBxSd2btKgvjj1vWXHQus\nkhEAjTtZI4Na3mlNMKMKhCb+Yiz+UirDP9vAkbOJ/PBoZ1rWKyU11dMuw8Fwqxrm7qWQdskaNeI3\nzOpLruHYrq65vx/mlR934lGrIh+PCKRVPR2rXuDOHoAdP1ijgmL+sNbV97MmrGnVD+q00WsCN0ET\nfzGVcDmNUV9sZMfxeP73QFtCWpbwmilZE5vsWmTdKHT5glXr3nuwVSCtYbtCTQTrD8Ty5LwtXLiU\nyqsDvBjWrpH2+ztK7H7r7uDdS+HoJkCsiWda9oPmvayzAp1n+Lpo4i+G4pNSGTtnM1F/nuej+wPo\n613f2SE5RlKcNXvV7iWw92drYpPy1a0jvtZ3W9MIOnE4YMzFy/xjfjTr9p+la4va/HuQNw2ra+li\nh7p4GvYut34EDoZblryA1wAAF0NJREFUU0uWKQ8enaFZT6usRq0WejaQB038xcyJ85cY/eUmjpxN\n4r/3+dPPtwQl/YwMOLXNmhlq/0prblrJgIq1rWqYrQeAx21FqhhYRobw1cYj/Gf5bgR4qlcLHujU\nhHJlSnFNn8KSkmhVDt3/Cxz4xZpvGKBKQ2gWYt0t3KQTVGuiPwRXyS3xl/hB4KFTo/hj/UkA0tMz\nCJ0axZ6NpwBITUkndGoU+yKseVIvX0ojdGoUB6LPAHApIYXQqVEc2hYLQGL8ZUKnRnFk51kALsYl\nEzo1iqN/xAEQH3OJ0KlRHN97DoBzpxIJnRrFyQPxAJw9nkDo1ChOH7Ym4I45epHQqVHEHL0IwOnD\nFwidGsWq348x4MN1SMxlJlWoQac6Vt/y8b3nCJ0aRXzMJQCO/hFH6NQoLsYlA3Bk51lCp0aRGH8Z\ngEPbYgmdGsWlBGsi7gPRZwidGsXlS2kA7Is4TejUKFJT0gHYs/EUoVOjSE/PAOCP9ScJnRpl+yx3\nrj3OomnRtuXt4cdY/MEW2/LWX46y9ONttuXon/9k+Yzt1rDLuINEfhnKildnwtSW8Fk3Ni/ew8r9\n/aDrs/C3VWxs8RO/nB0HzbqDqxu/hx4g7KvdtvbWLdjH6m/22JbXfruXtd/utS2v/mYP6xbssy2H\nfbWb30MP2JZ/mb2LjT8etC2v/HInm5cesi2v+HwHkT8dti0vn7Gd6J//BKyx/jWjL/BxcHPae9bg\nrWV/8Mazq/nm/3aSdfC0aFo0O9cet21fHL97Z48nAHDyQDyhU6M4dyoRcPJ3r2xFdp72ZtHe4fBE\nJDy5je1NP2dx7ERrmOjCR9j670ksfWY6fD8OImYSHRrB8k//+i5G/nSYFZ/vsC1vXnqIlV/utC1v\n/PEgv8zeZVsuSt89R9ChCkVIano6x84lMSd0G9XqVeTtPs05tuaUs8O6fhkZVomE49vh+EV47164\neAISBgOtwLsLNL8dDnrDOQPdvaztog/abbYoqFa+LDMfDGbN3hh+mbGD+ZuPMicmjgndmlIczp5L\nhOpNoLErxMfCY4esi8LLdsKBS9Z9A9u/hcS7Id0b5rwEtwTCmfaQWtPZkRcZ2tVTRGw4eJZ/hW7n\nYEwi9wQ25I2BXlQoW0x+ly+eguORVzyi4bJ1pEnFOla3jUdnazKTEtQvm54hLIw+zierD7D/TAKN\napTngQ4eDA5sQM1KWqLAKTLPLjmyLvO7GAVndlmF+QAq1fv/9s48Pqrq7OPfJ8lkIYQtgbDKJjsK\nGBZXXkVRxIVSl1JrYqVFxYKt1qXYV1+r1opr69vaflSsxYWIC8KnUmRVUcoaliRkgAAZSEhmkkz2\ndSZz3j/OzWSIgfIiZCbkfD+f+cx9zt1+eXLuM/eee85z9MQziaN0j6HEUdBtcNubQvMUMW38IUpG\nXhmvrNnPeruLft1ieGbG6NDtueOt0/nZXVngygTnXnBm6rt50BN2JI7SU/b1SYK+EyFhyDkT6E+E\nz6dYm+Xkja8Psd1Rgi1cmDoykZnj+nLFkIRTm9vXcPbw1EBBuv4ROJamxw4UZ+v3SgDhUdB9KPQY\nBYkjIX6IHlXcdUCbzzFkAn8I4W3wsc7u4r3NDjYeKKJzjI17Jg9i9mUDiYkMcpBQCiqdun+1+5Bu\nsik+qAN+cTYo3SZLmE1PxNFjJPQeB33H61GztvadKfSAs4IPtx3lk7RcSqo9dIgM56phPbh2VCKX\nDk6ge1zbDiTnDJ5andPJubfpJsa1V8873IiE6RHF8efrp4L4wXocSee++hPdOeRvakzgDzINPsW2\nHDerMgr4V0Y+zvI6enaK5ieTzuOuywbQKbqVerA0eKGyAMqPQVkulOfpkZTlueDO0cHeU9W0fViE\n7i2RMFTfDTU+HsefH1K9bkKNeq+PzYeK+SKzgC8ynRRV6peeQ3p05JLB8UwY0I0L+nSmf3wHMy4g\nlKh262ug+GDTTU9xti6rKz9+28i4ph+BwE/HHrqJs2MidOgW1Nnc2m2vHkdyCqWfLgNAeTw4klMo\nW7ECAF9NDY7kFMpXrgSgoaJC26tXA+AtKcGRnELF+g3aLizEkZxC5caNAHjy83Ekp1C1aRMA9UeP\nanvrVuq9PjI272Hzzbfz1B8+YPyza3jspWWMfOExrhE3f7sziXU39+Tmd54h8rDunlaTno4jOYXa\n/bq3QHXaThzJKdQd0m//q7ZuxZGcQv3Ro9retAlHcgqe3KNQUUDl8ndx3HYz3q/fhn+/TsUf78Ux\n/RK8i26Dt66hfP4IHFcNo2HhaFg0lfJX5uJ47FV8WxdD4T7KcmJwbBqEunYh3PkJpYNfxHFgOjyQ\nBnekUlI8HMcrn0OPERBuw/3BBxyZc4/f1+7Fizk6936/XbzobXLnP+C3i954k7yHHvLbha+/Tt4j\njzbZr73GsQWP+23Xy6+Q/8STftu58AUKnn7abxc89xwFzz3XZD/9NM6FL/jt/CeexPXyK3772ILH\nKXztNb+d98ijFL7+epP90EMUvfGm386d/wDFi97220fn3o978WK/fWTOPbg/+MBvO+6+m5KlSwGI\njAij/zO/5hGVzZbHr2b5vZNYsvcdpual8fGOXB5+dwtbZtzOvT97nh+/sZnnP9rG1h/8iO2LP8VV\nXovH7T7tugdQd+gwjuQUqtN0L6za/ftxJKdQk56u7awsXdey9GjZ0657+foOuXLjRhzJKXgLCwGo\nWL9B2yW6l1H56tU4klNoqNC9iMpXrsSRnIKvRvcSKluxAkdyCsrjAaD002U4klP8vi1ZuhTH3Xf7\n7bNW9zp0g77jca3NI399Ldy6CO79CmfYPAoa7oefr4Pb3qGgaBoFOWP0U0CVi4JFK3G+/CdYdi+8\nO5P82dNxJY+DZxLgpaEcmzmWwp9fAcvmwuonyLvrJgp/OwcyP4NDX5I3dzZFr72oU5Mo9Z26d6YJ\nyhsNEZkG/AkIB95SSj1/ts5ld9uxudKYwkw8Pg92t51I506u4mZqvDXY3XZiXLuZzHQq6yuxu+3E\nFu7hcq6lrLYUu9tOXFE6l3IV7lo3dredLkWZTOIKnJUustx2ag+mER47gEN7t9PfmcnKZSvZsLyI\nxKosflmVTXZpNlOSRpE0qpRODhc/vjyS0SMSyNr0LUfcWVTnbWFE1wYOHlpLXlEGdfbPGFo3iAO7\nv6GgcDfejQsZnBWLPSOLIucRWHon/aPr2JtThjtfYfvzOHpHe8gsjqPU3ZGYVY/QI9JLelFnKupj\n6VjmIz6hJ3vi+1EV46TL1Pl07jOSXWtXU+P8ioQHVxHbKZ60N39Hfcbn9EpKITKqA2lrn8Dj3kfj\nhIRpzjQ8xVl+e0fBDrzFGZxn2dsLtuMtSqcx08q2gm34CrPo67e34nMdok/gelfu8bazkN4Btior\n50b/8beh6uoCbP0UGGhLVBQ3NOpz7kBqO/ntNGcaYdKd6Za907WTsJhCv73LtZuwLhVczxwA9hTu\nIazAwzRmA5BelE5EQQTXogNSZnEGEQVxTOUOALKKs7A5E7ma24+ve2EzGdG7AxsaHEwYPpoHZ1/L\nnoNHyc9wMbBPEf+u9/LhjkMMrjjAim/XsnFvFD2lmEfzM9m6bhVSGk9CQz7DCrOotG9h5MAL8LqO\n4nLbiS/aywQuJb8yH7vbToJ7H0lMJLcyl2y3ndKSA4xhHEfKj3DYbaei9CCjuYDDZTkccdupLsth\nBCM4WHqQPLeduvIjDGUoB0oOUOC2463MZTADsbv3UeS2Q2U+/enH3uK9uN12bNWF9KYXmUWZlLrt\nxNS66UF30ovSqXDb6VhbSjxd2VO4hyq3nS71lXQmjl2u3dS47SR4a4glhjTnTurddnr5PERiI82V\nhsdtD6G6t13Xvb5/gL7j2R72LkRHceOs9/X63TcjkTZumLcQqlzsyFmAxIRzwxVToNJJ2taNhDWU\nM/3w11BVyM7SLoT5Mpn+kb5R2JWbSFjVl1zvfhbCIthzuAdhteuZ5nsPfvKx/kE6g7R64BeRcOAv\nwFQgF9gmIiuUUntPvufpkTp/FDPOT9JGeDhL5o1kxqALqKmqpMZbz3tzh3JD737kHNyHu7KYRT/t\nx5TOYYRv+JySmmLeuCOByzzHyH/nVYpr3Sz7YQeSjvybnb9Px+0t46sbw5h0ZBVD9m0gOqKav98i\n3Fa9kUdlK2V96vjfMfCwZyVjCz7jgK+G52bArzfNhXV3IZE2Um/qymNbH4ZvPBAZSeqMLjye/gKk\neVBRkaT+oAtP5n0Kzo74YuNI/bGNp8M6QHQ/vIk+UscdY0yP26HzeXi8JaQ6N5M0/lHoNoT6wl2k\nZr3LxCtfgeiu1DrWknrx+1x62c8gMo5qm48PBxUzuYMehVo55SI+7ZfDFJtuwim/JonlA3K5zvJl\nyXXjWTWsiGmWXTx9Al9eWMX1lu26cSJbkpQ/kBbMmMTuS6P9dt7MSexzd/EH4iO3TCKnPNF/cR26\nbRIFVQV++8CsSZTWlfrtrDsmUdtQ67cz75wENAX+XSkTiQ6P9h9/+08n0CWqi78ubJ49np6xPf32\nNz9PYkCnAX77yzkXMaxb0wTia+4dx5juY/z2v+4by6ReE/328vsv5Mq+E/z2x/NGM21A01N1YN0T\nm43U+aP44ZCLsIWHMXJQD/78q9H8aNhUFgy8nLLacuau/YKLE65mqhpFljOfl4YPJLr6PMr3uiiu\nKSH65l7UF4TR8OdvkYhSom/oiXdPFXG71xDXsYzqW/rSK9dHj39sQ9kqyJ41gAvLIjjvCzu1CJtS\nBjPFG0vmtiMUNXTgi7uHMCMsjny7k7zYeD6bM5SUmK7U5pZyuHcfUu8dztyOXZHCSo4NHMCS+0bw\nYFxXbKU1FA4fwgf3j+DxuM5EV9VTOmY47/9iJMPjOlNd76VywmiWxI1iXKdOeBt8VF16IUviM5kU\nG4vPp6icPJaPeu7niuholFLnTt1LOB8Szmf7PVfpupf0K133uv23rnvj5um699UjDIjpAf2nQ00J\nXyb9lWG2LhA3DGpKWDPkK8aoSGjoABFnPk1Fq7fxi8glwFNKqessewGAUuoPJ9rndNv40168iRGV\nmwnHRxg+IsR3urJPSINEoMKjICKKMFs0YRFR+h8VEWl9R4EtVmePtMXoZVsMRFrftg4By43rOujy\nqE56Emtbh5B/iWQ4u9R7fbgqanGW11JS5aG0xkNpdT0l1fWUVnsorfZQXuuhpr6BqvoGauq9VNc3\nUFPfQLWngQZf6L/La05jlZfjyuS4ssDLQjh+h+P3O36btnQ5ffvYFLqeZjbeUJqBqw9wNMDOBSY1\n30hE7gEaG/EqRWRf821OkQSg6DT3bU3ags62oBGMzjNNW9DZFjTCaejs9sz3Ol//lgpDdtSCUuoN\n4I3vexwR2d7SL16o0RZ0tgWNYHSeadqCzragEUJHZzB69eQBgTMt9LXKDAaDwdAKBCPwbwOGiMhA\nEYkEZgErgqDDYDAY2iWt3tSjlPKKyDzgC3R3zreVUpn/Ybfvw/duLmol2oLOtqARjM4zTVvQ2RY0\nQojobBMjdw0Gg8Fw5jjnR+4aDAaD4XhM4DcYDIZ2xjkd+EVkmojsE5FsEflNsPU0IiI5IpIuIrtE\nZLtV1k1E1ojIAeu7axB0vS0iLhHJCChrUZdoXrN8u0dELgqyzqdEJM/y6S4RmR6wboGlc5+IXNfy\nUc+4xn4iskFE9opIpoj80ioPKX+eRGeo+TNaRLaKyG5L5++s8oEissXS86HVYQQRibLsbGv9gCBq\nfEdEDgf4cqxVHrRrCKXUOflBvzg+CAwCIoHdwMhg67K05QAJzcpeAH5jLf8GWBgEXZOBi4CM/6QL\nmA78Cz1A8mJgS5B1PgU83MK2I63/fRQw0KoT4a2gsRdwkbUcB+y3tISUP0+iM9T8KUBHa9kGbLH8\ntBSYZZX/DZhrLd8P/M1angV8GESN7wC3trB90K6hc/mOfyKQrZQ6pJSqB1KBGUHWdDJmAP+wlv8B\n/KC1BSilvgbczYpPpGsGsFhpNgNdRKRVZoQ/gc4TMQNIVUrVKaUOA9nounFWUUrlK6XSrOUKIAs9\naj2k/HkSnSciWP5USqlKy7RZHwVMAT62ypv7s9HPHwNXi5zdRA0n0XgignYNncuBv6XUECer0K2J\nAlaLyA4rNQVAolKqcRaIAiAxONK+w4l0haJ/51mPzG8HNJUFXafVzDAOfQcYsv5sphNCzJ8iEi4i\nuwAXsAb9tFGqlPK2oMWv01pfBpz1SXeba1RKNfry95YvXxWRxtl4gubLcznwhzKXK6UuAq4HfiEi\nkwNXKv0cGHL9bENVl8VfgcHAWCAfeDm4cjQi0hH4BPiVUuq4mTxCyZ8t6Aw5fyqlGpRSY9Gj/ScC\nw4Ms6Ts01ygio4EFaK0TgG7AY0GUCJzbgT9kU0MopfKsbxewDF2JnY2Peda3K3gKj+NEukLKv0op\np3XR+YA3aWp+CJpOEbGhg+n7SqlPreKQ82dLOkPRn40opUqBDcAl6OaRxoGogVr8Oq31nYHiIGic\nZjWnKaVUHfB3QsCX53LgD8nUECISKyJxjcvAtUAGWttd1mZ3AcuDo/A7nEjXCiDF6plwMVAW0ITR\n6jRrG52J9ilonbOsXh4DgSHA1lbQI8AiIEsp9UrAqpDy54l0hqA/u4tIF2s5Bj2fRxY6uN5qbdbc\nn41+vhVYbz1htbZGe8APvaDfQQT6MjjXUGu9RQ7GB/3WfD+6LfC3wdZjaRqE7hWxG8hs1IVuf1wH\nHADWAt2CoG0J+rHeg25v/NmJdKF7IvzF8m06MD7IOt+1dOxBX1C9Arb/raVzH3B9K2m8HN2MswfY\nZX2mh5o/T6Iz1Px5IbDT0pMBPGmVD0L/8GQDHwFRVnm0ZWdb6wcFUeN6y5cZwHs09fwJ2jVkUjYY\nDAZDO+NcbuoxGAwGQwuYwG8wGAztDBP4DQaDoZ1hAr/BYDC0M0zgNxgMhnaGCfyGcwYRiQ/IgFjQ\nLLvkprN0znEisugE63JEJOEMnitVRIacqeMZ2i+mO6fhnEREngIqlVIvneXzfAQ8q5Ta3cK6HHTf\n7KIzdK7/Au5USs05E8cztF/MHb+hXSAildb3lSLylYgsF5FDIvK8iPzEyqOeLiKDre26i8gnIrLN\n+lzWwjHjgAsbg771xLHaysX+FnqATuO2n1lJ+TIbE/OJyGwR+WPANnOsJF6xIvK56LzuGSLyI2uT\njcA1ASkKDIbTwgR+Q3tkDHAfMAJIBoYqpSYCbwHzrW3+BLyqlJoA3GKta854mobfA/wP8I1SahQ6\nB9N5AetmK6WSrH0eEJF4dC75m6xcOQB3A28D04BjSqkxSqnRwCoApfPmZFv6DYbTxtw5GNoj25SV\nE0VEDgKrrfJ04Cpr+RpgpDSlcO8kIh1VU7510JOYFAbYk4EfAiilPheRkoB1D4jITGu5HzBEKbVZ\nRNYDN4pIFmBTSqWLSB3wsogsBP6plNoYcBwX0BvYcdp/vaHdYwK/oT1SF7DsC7B9NF0TYcDFSqna\nkxynBp0T5qSIyJXoH5JLlFLVIvJlwH5vAY8DdnTmRpRS+0VPwzcdeFZE1imlnra2j7bOazCcNqap\nx2BomdU0Nfsg1jypzcgCzg+wvwbusLa/HmicvKQzUGIF/eHoafYAUHqijn7WfkusfXsD1Uqp94AX\n0dNMNjKU45uXDIb/N+aO32BomQeAv4jIHvR18jX6vYAfpZRdRDqLSJzS0xb+DlgiIpnAJuCItekq\n4D6rOWcfsLnZuZYCY5VSjU1DFwAviogPnYF0LoCIJAI1SqmCM/y3GtoZpjunwfA9EJEHgQqlVEsv\nf0/1GP9Ev0hedwrnKldKtThuwGA4VUxTj8Hw/fgrx78zOGVEpIuI7EffxZ806FuU0jSBuMFw2pg7\nfoPBYGhnmDt+g8FgaGeYwG8wGAztDBP4DQaDoZ1hAr/BYDC0M0zgNxgMhnbG/wHn4zRi8wZ4TAAA\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Capacity for mechanical ventilation is filled by COVID19 patients after 54.8 (conventional), 84.8 (contingency) and 122.6 (crisis) days\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8CZIMEGwdcuE",
        "colab_type": "text"
      },
      "source": [
        "Interpretation: While interventions that reduce infectiousness do \"flatten the curve\", cases are still WAY over hospital capacity. There is no way to get anywhere close to staying under hospital bed capacity or mechanical ventilation capacity without reducing $R_0<1$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "FswTJm06ERag"
      },
      "source": [
        "### Assumptions 2\n",
        "* All cases go to the hospital\n",
        "* All critical cases require ICU care and mechanical ventilation\n",
        "\n",
        "Note: No point running this scenario because it would be even more extreme than Assumption 1 (mild cases stayed home) and Assumption 1 already lead to rapid overlow of hospital resources"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "9vCkYHEUEZct"
      },
      "source": [
        "\n",
        "### Assumptions 3\n",
        "* Only severe or critical cases go to the hospital\n",
        "* All critical cases require ICU care and mechanical ventilation\n",
        "* When hospital capacity is exceed, individual dies\n",
        "\n",
        "Note: Could be used to simulate expected increases in death if capacity exceeded\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UjnSgntDdEEA",
        "colab_type": "text"
      },
      "source": [
        "## Alternative Models\n",
        "\n",
        "To be continued, including\n",
        "* Assuming ~30% of cases are asymptomatic (as seen on Diamond Princess) (This would lead to a re-interpretation of the reported rates of severe and critical infection, so the prevalence of these stages would decrease)\n",
        "* A parallel instead of series model of disease course (because it is unclear if it is realistic that individuals who pass through the mild stage on the way to a severe state spend as long in the mild stage as individuals who never progress)\n",
        "* Including pre-symptomatic transmission (for about last ~2 days of exposed period, as estimated in some studies)"
      ]
    }
  ]
}